The very first mention of Castiel comes in season 3, when he is one of the beings mentioned at the start of the invocation Sam reads over the grave of the sea captain in Red Sky At Morning. (I haven't found a transcript of the invocation, but it appears to start by calling on "Aziel, Castiel, Lemistiel...".) "Red Sky At Morning" is the only episode of Supernatural which was written by Laurence Andries, who is otherwise listed as a consulting producer on Season 3 of Supernatural for the episodes before the writers' strike. Neither he nor anyone else can have known what he was starting.
"What know we of the Blest above but that they sing, and that they love?" (William Wordsworth)
The big difficulty in understanding Castiel is how little information we have about him. We are shown few of Castiel's interactions with anyone except Dean, or with various fallen or disobedient (and therefore largely unreliable) angels. Apart from Dean, there's no-one who talks about Castiel when he's not around, and there's almost no information about what Castiel has been doing and who he has been with. In It's the Great Pumpkin, Sam Winchester, when Sam is introduced to Castiel Sam says "I've heard a lot about you". Really? Sam may have heard a lot from Dean about what Castiel has done, but what could he have heard about Castiel himself? Even when we look at what Castiel has said and done, his statements and actions for most of his time on earth have been compromised by the orders he has been given, and by disarray, dissention and disobedience amongst the angelic host. He's beautiful, and he's an enigma.
The basic biographical facts of Castiel's life are pretty sketchy. In On The Head Of A Pin, Uriel reminds Castiel of Lucifer: "you do remember him". In order to remember Lucifer, Castiel must have been created by the time of the Fall, when Lucifer left heaven. So he's been around a long time.
Address: no fixed abode
"It is not known precisely where angels dwell - whether in the air, the void, or the planets. It has not been God's pleasure that we should be informed of their abode" (Voltaire)
Every time we see Castiel he is operating in an alien, unfamiliar environment - Earth. It's implied in The Rapture that Castiel has stayed in the body of Jimmy Novak all the time between Lazarus Rising and the battle between the angels at the start of The Rapture, so he hasn't been home to heaven in all that time. Then his period back home in heaven is a relatively brief, but obviously distressing period of "re-education" intended to negate all Castiel has learnt of humans, and in particular of Dean. Since the start of season 5, Castiel has been wholly exiled from his home in heaven. Who can forget that scene in The End of Castiel standing by the side of a road, with nowhere to go and no-one to spend time with, waiting for Dean to snatch the sleep he so desperately needs? First we're laughing over the Voice telling Castiel he's almost out of minutes, then we're given that haunting image of loneliness.
Occupation: warrior of God
In "Are You There God?..." Castiel is clear that he is not a fluffy-winged guardian: "Angels are warriers of God. I am a soldier". He displays some strong military traits, too: obedience to orders, and loyalty to his fellow soldiers, his brothers in arms.
"In Heaven, an angel is nobody in particular" (George Bernard Shaw)
As a soldier, Castiel seems to be pretty low down in the ranks. He's an angel rather than an archangel. Even as an angel he is ranked lower in the garrison than Anna and Zachariah. In Its The Great Pumpkin, Sam Winchester Castiel is apparently in charge of Uriel. But Castiel is only just in control: in Castiel's presence Uriel feels free both to get close to blaspheming (calling the humans, who are God's creation, "mud monkeys" and "plumbing on two legs") and to propose disobedience to the two angels true orders (when Castiel says "its out of our hands" Uriel replies "it doesn't have to be"). So even at this stage Uriel is not much in fear of Castiel's authority. By the time of On The Head Of A Pin Uriel is giving orders to Castiel. Castiel is left isolated at the bottom of the chain of angelic orders, not being told much and with no power to require other angels to act with him.
"Are You Experienced?" (Jimmy Hendrix)
Castiel is inexperienced in fighting: neither he nor any other angel has been to earth in order to fight in a very long time. As he says in Are You There, God?, "we're here walking among you now for the first time in 2,000 years." So even if Castiel's nature is to be a soldier, and he is trained to be a soldier, he has had no recent experience of fighting on earth, and perhaps no experience of fighting at all before raising Dean out of hell. It shows. Castiel's first fight on earth comes in Heaven and Hell, and he fails. He was losing his fight against Alistair, and was saved by Anna. Then he fights Alistair again in On the Head Of A Pin, and is saved by Sam. He loses his fight against Uriel in On the Head of a Pin and is saved by Anna again. He loses his fight against other angels before being taken back to heaven at the start of The Rapture.
Castiel's first fighting success comes later in The Rapture, when he kills two minor demons. He is then ruthless in killing Zachariah's two sidekicks in Sympathy for the Devil. He is vanquished by a much stronger power, the anti-Christ, Jesse, in I Believe the Children Are Our Future, when he is turned into a miniature action figure. It's clear all the way through, though, that Castiel has courage, shown when he takes on opponents such as Raphael, Jesse and Gabriel that he knows are stronger than he is. Eventually this attitude pays off and Castiel begins to learn how to fight effectively even though his angelic powers are diminishing. He cleverly and ruthlessly uses Meg as a bridge to get out of the circle of holy oil in Abandon All Hope, and successfully stands up to Lucifer, escaping safely with Sam and Dean. It's been a steep learning curve for him.
Castiel and the humans
"It is by means of spirits that all the intercourse and communication of gods with men, both in waking life and in sleep, is carried on" (Socrates)
Castiel is also inexperienced in dealing with the humans. There is an implication, from Anna in Heaven and Hell when she refers to being in the same foxhole as Castiel and Uriel, and from Uriel in On The Head Of A Pin when he is tempting Castiel to disobedience, that Castiel, along with Anna and Uriel, has been one of the angels watching over the Earth. But observing is not doing, and Castiel's lack of practical experience on Earth is evident early on. We are first shown him in Lazarus Rising when he unsuccessfully tries to contact Dean using his true voice. He fails, and after his second attempt Dean's ears are left bleeding. As he acknowledges to Dean; "This was my mistake". It's a mistake based on inexperience, and on the assumption that Dean is special: he is of course, but not in the way Castiel first thought. And that fact that Dean can't be contacted using Castiel's real voice means that Castiel has to come down among the humans in physical form in order to carry out his mission.
Not only is Castiel inexperienced in dealing with the humans, he has an alien's perspective on humans. At the start of Season 4, when Castiel first comes down to earth, his view of humans is wholly derived from the fact that they are God's creation: it's an objective, intellection appreciation based solely on that divine origin. "These people, they're all my father's creations. They are works of art." (Castiel in It's the Great Pumpkin, Sam Winchester). There's nothing personal in this description, and it's not an opinion formed on direct experience or independent thought, it's an opinion based solely on Castiel's faith in his God. (The alternate, future, disillusioned Castiel in The End has a slightly less flattering assessment of humans: congratulated by Dean on joining the human club he says "I used to belong to a much better club".)
Castiel's God-centric view of humans is challenged pretty early on, by Dean's snark in Are You There, God? It's Me, Dean Winchester. Dean says angels are dicks, doubts the existence of God, and is sarcastic about the help the angels provided to deal with the witnesses. This human isn't falling into line with the plans which Castiel has orders to follow, and Castiel's response is clear: "You should show me some respect. I dragged you out of hell, I can throw you back in." But for Castiel to put Dean back in hell without orders to do so would be disobedience. And for Castiel to suggest that it would be his own choice to throw Dean back into hell is to abrogate to himself a decision which is God's, which is also disobedience. So within three days of Castiel rescuing Dean from hell and coming down to earth, Dean has got under his skin to the extent of Castiel's suggesting something which is the angel's biggest crime, their "Murder One". It's an early indication that Castiel's new job out among the humans is going to be harder, and more testing, than he could ever have contemplated when in the safety of heaven.